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Author Topic: How much energy is required to continualy orbit the Earth in less than 84 minute  (Read 9792 times)

Offline Geezer

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Puck does a constant speed but it is velocity we are concerned with energy is constantly required to divert his natural hyperbolic path that would take him out Earth orbit to a circular one around the Earth

We can calculate the required force to maintain the path, but as JP points out, without some information about the nature of the thing (presumably it's some sort of rocket) that's producing the force, I don't think we can get at the energy consumed.

Also, if it is a rocket, I have a suspicion that it will need to exhaust a good bit more than a kilogram of matter for every kilogram of Puck's mass during a circuit, so, as we have to account for the changing mass of the fuel, the force will be far from constant and the math is going to become rather tricky.

It's not rocket science, er, well, I suppose it really is.
« Last Edit: 14/05/2010 20:39:13 by Geezer »
 

Offline syhprum

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The calculation has been done for a photon drive and comes out at 10^10 Watts but of course photon drives are only efficient driving high speed vehicles and the velocity increment applied to Puck in the direction of the centre of the Earth is very low compared with the the velocity of the emitted photons.
If my estimate of the required power as 44.75 MW is correct the efficiency is .045%.

I did only ask how much power was required not how it was generated. 
« Last Edit: 15/05/2010 08:56:56 by syhprum »
 

Offline syhprum

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An interesting question arises would it be possible with available technology to actually do an orbit of the Earth including take of and landing in 40 minutes, I don't think it could be done.
 

Offline Geezer

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I did only ask how much power was required not how it was generated.
 

In reality, would it not have to be far greater than that? I think the only way we could produce the force would be with a rocket, but the rocket would also have to transport its fuel, so the required thrust would also have to account for the mass of the fuel which I think will be much greater than the mass of Puck.

I think you're estimate might be off by a couple of orders of magnitude.
 

Offline syhprum

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I was only concerned with how much power was required to maintan the orbit not to design a system to produce the power, as you say it would require a large rocket which in turn would have to generate a great deal of power to orbit its own mass and fuel.
 

Offline Bored chemist

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In summary, if you use the most efficient means to achieve the stated task then the energy is zero and if you use a less efficient means then the answer is "it depends".
 

Offline syhprum

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Can't argue with that !
 

Offline tommya300

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The attempt to, of the intended event is in question. Not the fact that the attempt of the intended event was successful!
For the event to be successful the duration needed to be at least longer then 84 minutes.
Therefore the orbit was not accomplished and nothing is needed to sustain the failed event.
Like in baseball I through the ball to the outfield, in Yellowstone Park,
 (big ball park)! Can we assume I was successful in making it reach the outfield?

"An orbit is a regular, repeating path that one object in space takes around another one."
« Last Edit: 19/05/2010 10:42:37 by tommya300 »
 

Offline imatfaal

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mmm - not sure about this one.  cannot see any holes in arguments, but still...
 

Offline Bored chemist

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I think tommya means that this
"An interesting question arises would it be possible with available technology to actually do an orbit of the Earth including take of and landing in 40 minutes, I don't think it could be done."
wouldn't be an orbit because it's a one-off.

Incidentally, I gather that bored researchers at the North and South poles fill in time by having races round the world.
With a bit of messing about (like getting to the Arctic), you could walk round the world in 84 mins, if you jumped in the air at the start and finish of this circumnavigation would that count as take off and landing?
 

Offline wolfekeeper

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FWIW 44 minutes is probably much too quick for humans- the g-forces get ridiculous, if you include acceleration and deceleration time, the g-force really mounts, IRC you're hanging upside down pulling 10g for most of it- not my idea of fun!
 

Offline Bored chemist

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So, you didn't read the bit about being able to walk round the world in less than 84 minutes?
 

Offline wolfekeeper

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That's not an orbit.
 

Offline Bored chemist

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Nor's the original post's question.
 

Offline daveshorts

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Just to make it more complex, if the energy or reaction mass supply for puck's rocket are carried on him, his mass will change as he orbits. Even with photon drives, his mass is going to decrease as it fires a bit. So you have to solve a fun differential equation.

Essentially
a = F/m

F= (g Isp /m)  dm/dt

m = mass of fuel
a = acceleration required = 33.45 m/s2
Isp = figure of merit for your rocket engine for shuttle = 450s
g = earth's gravitational field (from defintition of ISP) = 9.81

if you integrate those up you get
m = eat/gIsp

so if he has to orbit for 40mins = 2400s
m = e18.2
  = 80 000 000kg of rocket per kg of puck

As this is hydrogen oxygen fuel the energy is going to be silly at anout 285kJ/mol of water formed this will use of the order of 1 x 1015J /kg of puck

You would be better off using something with a higher Isp like an ion engine using an ion thruster with an Isp of around 3000 you would only need 15kg of fuel per kg of puck. The energy required will be the integral of the force times about 40kW/N

so I get about 340MJ/kg

which may or may not be right according to my ability to integrate.
 

Offline syhprum

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I only really wanted to calculate how much power was required, I had not got as far as devising a system to generate it.
Many thanks for your heroic computation.

Gino (syhprum)
 

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